Answer:
The Triangle Inequality Theorem
Note: The Sum of the two lengths must be greater than the third length, therefore a Triangle can be constructed.
a+b>c
a+b>ca+c>b
a+b>ca+c>b b+c>a
Let A be the first length
B the second length and;
C the third length
Given
1. 5, 7, 13 | We Can't Make a Triangle with this given numbers, so FALSE
Solve:
5+7 < 13
12 < 13 ❎
5+13 > 7
18 > 7 ✔️
7+13 > 5
20 > 5 ✔️
2. 5, 9, 12 | TRUE
5+9 > 12
14 > 12 ✔️
5 + 13 > 9
18 > 9 ✔️
9 + 12 > 5
21 > 5 ✔️
3. 10, 15, 25 | FALSE
10 + 15 = 25
25 = 25 ❎
10 + 25 > 15
35 > 15 ✔️
15 + 25 > 10
40 > 10 ✔️
4. 1, 2, 3 | FALSE
1 + 2 = 3
3=3 ❎
1 + 3 > 2
4 > 2 ✔️
3 + 2 > 1
5 > 1 ✔️
5. 6, 10, 5 | TRUE
6+10>5
16>5 ✔️
6+5>10
11>10 ✔️
10+5>6
15>6 ✔️
Step-by-step explanation:
Just Follow the Formula and you'll get the answer too.
